In the open plan offices of BBC Radio 1, two desks sit side by side. One is yellow and round and belongs to the boss Andy Parfitt, 50, the BBC's head of popular music. The desk has a pint glass on it, filled with water. The adjoining work station belongs to his protégé Ben Cooper, 39. It has a surfboard next to it and a pinned-up notice containing buzz words including "passionate", "entertaining" and "young".

The two executives, who are in an adjoining office waiting to be interviewed by The Independent, have a difficult job that Cooper later describes as "like walking a tightrope in high heels". Their task is to find a way to engage a target audience of 15 to 29-year-olds in a medium once known as "The Wireless".

Radio 1's average age is now 33, to the consternation of a deeply threatened commercial sector, which says it sounds too grown-up, too much like Radio 2. Both services should be privatised say some media executives. And just as Radio 1 – still often referred to as "the nation's favourite" – attempts to justify its public funding with programmes that educate young people, star presenter Chris Moyles is castigated by the broadcasting watchdog Ofcom for "offensive and derogatory" comments about the sexuality of the singer Will Young.

So it's perhaps not so surprising when Parfitt makes a statement that, from any other radio head, would be quite stunning; namely, that he doesn't envisage his network growing. "Radio 1 probably won't get any bigger than it is at the moment, at 10.5-11 million," he says. "We are acutely aware of the balance that we've got to achieve and we are not in the business of just putting on audience for audience sake."

Given that Parfitt and Cooper have ambitious plans for Radio 1 and its digital sister station, the black music-focused 1Xtra, does this mean they are prepared to jettison older listeners? "If that's the way it worked out then nobody here would be panicking," says Parfitt. "Our job is to reach young audiences but I don't ask Ben to deliberately make a 32-year-old go away. The important thing is we are not targeting that group."

As Cooper explains, with a tinge of frustration, "people refuse to grow old these days". "Ben is right," chips in his mentor. "It's an absolutely clear societal shift, music tastes have converged and people want to remain young longer. We are not targeting the over-thirties."

Parfitt was appointed controller of Radio 1 more than 11 years ago. In some quarters he was expected to succeed Jenny Abramsky as BBC head of radio and, though that job went to the BBC marketing chief Tim Davie, Parfitt's fat portfolio makes him almost as powerful. Aside from heading up the BBC's popular music output across all media, he runs Radio 1, 1Xtra, BBC Asian Network and the multi-platform youth offering BBC Switch. "I've got a long business card," he jokes.

Cooper began work as deputy controller of Radio 1 and 1Xtra last week and is intent on bringing the networks closer together. He hopes to emulate Harry Beck, the designer of the London Tube map, and make the schedules look simpler. "There's this mess, this whole endless stream of things for us to consume and if you can make your schedule as clear as possible to navigate, then you should be able to build audiences," he says.

The 1Xtra audience – some 533,000 strong – has not received the boost from digital radio (DAB) that was anticipated. "You look at young people and they're not the ones buying DAB sets, it's my mum in John Lewis," admits Cooper. "Young people are consuming 1Xtra through digital TV and listening online, both very static places to listen to radio, whereas a lot of radio gets listened to in the car or on your headphones on the bus, and that's the challenge."

When Parfitt pointedly gives a vote of confidence to DAB as "the radio broadcasting platform of the future", a big cheer breaks out. It turns out to be for Whoopi Goldberg, who is leaving the building after a guest appearance on Moyles's show.

Despite the commitment to DAB, trials have been underway at Radio 1's Yalding House headquarters in central London, to make radio more of a visual medium, a project partly inspired by Parfitt's visit to Korea a couple of years ago. "The deep insight we are working from is that the audiences to 1Xtra and the younger end of Radio 1 simply expect to see and hear their media brands. The idea of being simply an audio brand is wrong," says Parfitt, pointing out that all modern media devices come with high-quality screens. "If there's not something on that which enhances the audio broadcast or podcast then in the future you won't be in the game. Ben has spent a lot of time working on what a visualised Radio 1 and 1Xtra looks like and there have been some exciting trials. Video streaming from studios is just half of it, there's artist information, images, text messages floating across the screen, tweets, all kinds of graphical information."

The tweets of Twitter are an awkward subject for Parfitt, as he's been cloned on that instant messaging website by a well-informed though "fake" twitterer, who lampoons his long list of job titles, saying "I rest on Sundays". The fraudulent tweeter makes reference to the new Radio 2 and 6 Music controller Bob Shennan: "So, Bob's going for non-stop Glasto on 6 [Music] is he? Trying to out do me, the King of Pop! This is war!"

The real Parfitt is not impressed by claims that Radio 1 and Radio 2 sound similar. "I really reject that notion. Just looking at the facts, of the 900 tracks that Radio 1 and Radio 2 play in the daytime, there's a crossover of about 36 tracks," he says. "If you spend the morning with Terry [Wogan], Ken [Bruce] and Jeremy [Vine], compared to Chris [Moyles], Jo [Whiley] and Edith [Bowman], they are worlds apart."

As soon as Moyles made his Will Young gaffe, Parfitt says the "mistake" was recognised and the presenter reprimanded. "A very clear conversation was had, and that was followed up in writing. Yes, [by] me. That's the controller's role, to absolutely take responsibility for what happened and make sure that it does not happen again," he says, before explaining that the network needs to take some risks. "We have to strive to be real and sometimes play the records that some people would be challenged by or employ talent that might sometimes give offence – I'm not talking about Chris here."

Parfitt promises "we've put steps in place to make sure it doesn't happen again" and Cooper adds that he too has been laying down the law. "It's my responsibility to talk to the executive producer of Chris's show and the production team. It's not just a one-off conversation between Andy and Chris." Cooper expressed his concerns immediately after the broadcast. "I'm not going to say whether I went in shouting and screaming or not, but we had a meeting about it."

If Moyles oversteps the mark again Parfitt "will deal with that when it arrives". He then rather unconvincingly compares the incident to an item on "body-piercing" by the Radio 1 current affairs team Newsbeat. "That might actually be a difficult listen for some people," he muses.

Nonetheless, it's clear that Radio 1's system of checks and balances worked far more effectively than Radio 2's, which was shown to be woefully inadequate over Sachsgate. After more than a decade in charge, Parfitt knows the Radio 1 audience inside out, having conducted vast amounts of market research into its listening habits. Members of staff are sent to "producer labs" to see at first hand the way that provincial youth live. "We chuck the producers down outside of London because we think that London is a separate country almost," says Cooper, who grew up in the Midlands market town of Bromsgrove. "They meet young listeners and spend a day looking at how they live their lives, how they use their computers and mobile phones."

Some are shocked to find how different they are from listeners, he says. "The female producer in her late twenties who lives alone in a small flat is seen as 'What's attractive about your life? You're living with a cat?'"

Those who question the presence of older presenters on these young networks (1Xtra, for example, is increasing the profile of the 51-year-old hip-hop DJ Tim Westwood) don't appreciate the full picture. Young listeners are often drawn to big-name presenters, says Parfitt, pointing at a Radio 1 poster on the wall. "There's John Peel, Annie Nightingale, [Pete] Tong, all of whom ... have [enjoyed] very young profiles and it's because of their status that they're beacons in an increasingly busy and fragmented environment. John had one of the youngest profiles of all the DJs when he was on Radio 1."

Moyles also has a younger audience than some might think, with 40 per cent of his listeners aged under 25. Westwood, who also has a youthful following, has impressed the Radio 1 chiefs with his YouTube channel TimWestwoodTV, which has clocked up one million channel views.

Radio 1 is a well-honed machine, or "rather a good proposition", as Parfitt puts it. More established "genre leader" presenters are juxtaposed with "exciting, new, energetic DJs", who are dropped onto the Radio 1 conveyor belt. That means young stars like Nick Grimshaw and Greg James at Radio 1 and Nottingham-born MistaJam at 1Xtra, who excites both bosses. "He's brilliant because he knows his music, he's able to mix, but he's entertaining and he's warm. Some specialist DJs tend to be quite cool, quite aloof," says Cooper. "Plus he's from outside London."

For six years Cooper has held senior executive positions at Radio 1 and for some time has been in charge of the day-to-day running of the network. He laughs when the question is asked as to why he has not been given the full controller's title.

What plans does Cooper have for Radio 1? He talks of the station being "entertaining and informative and educational" echoing some of those key words on his desk, "Reithian values but still very important". After a pause, he adds: "You've got to educate them in terms of citizenship and social action which I'm very keen to emphasise because I think young people are more political than you ever are in any other part of your life." You don't get that very often on Radio 2.